| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.86 |
| Score | 0% | 57% |
In a class of 21 students, 13 are taking German and 9 are taking Spanish. Of the students studying German or Spanish, 7 are taking both courses. How many students are not enrolled in either course?
| 19 | |
| 20 | |
| 6 | |
| 10 |
The number of students taking German or Spanish is 13 + 9 = 22. Of that group of 22, 7 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 22 - 7 = 15 who are taking at least one language. 21 - 15 = 6 students who are not taking either language.
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 20% off." If Alex buys two shirts, each with a regular price of $42, how much will he pay for both shirts?
| $33.60 | |
| $75.60 | |
| $63.00 | |
| $60.90 |
By buying two shirts, Alex will save $42 x \( \frac{20}{100} \) = \( \frac{$42 x 20}{100} \) = \( \frac{$840}{100} \) = $8.40 on the second shirt.
So, his total cost will be
$42.00 + ($42.00 - $8.40)
$42.00 + $33.60
$75.60
If \(\left|a\right| = 7\), which of the following best describes a?
a = 7 |
|
a = -7 |
|
a = 7 or a = -7 |
|
none of these is correct |
The absolute value is the positive magnitude of a particular number or variable and is indicated by two vertical lines: \(\left|-5\right| = 5\). In the case of a variable absolute value (\(\left|a\right| = 5\)) the value of a can be either positive or negative (a = -5 or a = 5).
What is \( \frac{6}{6} \) + \( \frac{8}{12} \)?
| 2 \( \frac{4}{9} \) | |
| 2 \( \frac{4}{12} \) | |
| 1 \( \frac{9}{12} \) | |
| 1\(\frac{2}{3}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 6 are [6, 12, 18, 24, 30, 36, 42, 48, 54, 60] and the first few multiples of 12 are [12, 24, 36, 48, 60, 72, 84, 96]. The first few multiples they share are [12, 24, 36, 48, 60] making 12 the smallest multiple 6 and 12 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{6 x 2}{6 x 2} \) + \( \frac{8 x 1}{12 x 1} \)
\( \frac{12}{12} \) + \( \frac{8}{12} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{12 + 8}{12} \) = \( \frac{20}{12} \) = 1\(\frac{2}{3}\)
What is \( 5 \)\( \sqrt{80} \) - \( 4 \)\( \sqrt{5} \)
| \( \sqrt{9} \) | |
| 16\( \sqrt{5} \) | |
| \( \sqrt{16} \) | |
| 20\( \sqrt{16} \) |
To subtract these radicals together their radicands must be the same:
5\( \sqrt{80} \) - 4\( \sqrt{5} \)
5\( \sqrt{16 \times 5} \) - 4\( \sqrt{5} \)
5\( \sqrt{4^2 \times 5} \) - 4\( \sqrt{5} \)
(5)(4)\( \sqrt{5} \) - 4\( \sqrt{5} \)
20\( \sqrt{5} \) - 4\( \sqrt{5} \)
Now that the radicands are identical, you can subtract them:
20\( \sqrt{5} \) - 4\( \sqrt{5} \)